The development of statistical methods to detect complex biological or genetic mechanisms is very important to the furthering of our knowledge of the etymology of complex diseases. One example where genes operate through complex biological mechanisms to increase disease risk is through an interaction between maternal and offspring genes termed maternal-fetal genotype (MFC) incompatibility. MFC incompatibility arises from maternal-fetal genotype combinations that predispose for maternal immunological processes that adversely affect the developing fetus, and thereby increase susceptibility to disease. Although the adverse environment takes place early in life, the effects of it can be studied decades later because of its genetic origins. Using population designs that collect only offspring and their mothers, interactions between mothers and offspring gene effects are confounded with the effects of a susceptibility risk allele in the offspring or the mother. To solve this problem, my research group developed the original MFG test to estimate MFC interaction effects by adapting the log-linear method for estimating genotypic relative risks for trios (parents and affected offspring). However, there are still some fundamental limitations to the current version of the MFG test that must be overcome. The current test is limited to 2-generation families, it can not handle all forms of MFG incompatibility and it can not be used with quantitative outcomes. This proposed work will expand upon existing statistical methodology (the MFG Test) that estimates disease relative risk for MFG incompatible offspring. Specifically this research will (1) Develop an extended MFG test (EMFG Test) to accommodate arbitrary family structures, (2) Generalize the EMFG test so that one statistical method can be used to fit a variety of MFG incompatibility models, (3) Allow for interactions between specific covariates and MFG incompatibility in the arbitrary family setting, (4) Extend the EMFG test for use with quantitative traits. PUBLIC HEALTH RELEVANCE: This proposed work is relevant to public health because it will provide new statistical methods that can be used by others to test for the joint effects of maternal and offspring genes in a wide range of diseases. Ultimately it will help the scientific community better understand the mechanisms by which environmental and genetic risk factors interact to increase risk to disease.